1. Field of the Invention
The present invention is related to the field of well drilling. In particular, the present invention provides a method and apparatus for determining the turning radius of a well drilled with a particular drilling assembly in a hydrocarbon formation.
2. Description of Related Art
Directional wells have been utilized in the petroleum industry for several decades. For example, directional wells have been used on offshore platforms to drill wells into locations that the laterally displaced from the location of the platform.
It has recently become more economical to fully develop known reserves, rather than attempt to locate new reserves. As a consequence, drilling from existing facilities has become increasingly important and hence, the ability to reach laterally-displaced locations has become increasingly important. Wells are frequently drilled today which deviate significantly from vertical (e.g., 45.degree. or more) and in many cases the prospect of drilling horizontal wells has become attractive. U.S. Pat. No. 4,789,032 describes one possible horizontal drilling method and apparatus and is incorporated herein by reference for all purposes.
In highly deviated wells, accurate planning is required to prevent damage to the drill bit, to ensure that the desired location is drilled, to prevent stuck drill pipe, and the like. In particular, it is important to be able to accurately predict the radius of curvature that will be produced by a given drilling assembly before the well is drilled. If the radius of curvature is not accurately predicted it may be necessary to change the bend of the drilling apparatus or to change the bend in the motor after drilling operations have commenced. This can be extremely expensive dure to lost rig time.
Interference has been recognized as an important parameter in predicting the radius of curvature that will be produced by a drilling assembly. As used herein, interference is intended to mean the lateral distance beyond the wellbore wall which an unstressed drilling assembly would extend, especially drill pipe using a bent sub or motor. FIG. 1 illustrates the interference of a bent drill assembly 2 in a wellbore 4.
An estimate of interference has been used to predict the turning radius of a wellbore, to predict the force applied by the bit on the well bore, and the like. Various methods have been proposed to determine interference in a wellbore and, further, to predict turning radius. For example, Maurer et al., "Selecting Pad Heights for the First Austin Chalk Drainhole Field Test", May 30, 1985, described one possible method of predicting interference. Maurer et al. propose a method in which interference is determined based upon the equation: EQU I=h+1/2DM+L Sin .theta.1/2DB-DH (1)
where:
I=interference (in inches) PA1 h=pad height (in inches) PA1 DM=motor diameter (in inches) PA1 .theta.=bend angle PA1 DB=bit diameter (in inches) PA1 DH=hole diameter (in inches) PA1 L=length from bend to bit (in inches)
Maurer then plots hole radius as a linear function of interference and uses this function to predict the turning radius of future wells.
It has been found by the inventor herein that the method proposed by Maurer et al. produces unreliable results in predicting deviated well performance. Specifically, it has been found that when actual well radius is correlated with the predicted radius using the Maurer relationship, the data do not correlate or correlate very poorly. In particular, the rate of turn was found in some cases to vary over 6.degree. from the predicted value (or about 50%). Therefore, the interference prediction in Maurer et al. is useful only in a qualitative sense, and does not provide a quantitative prediction of turn radius. In particular, it has been found that two holes having the same turning radius might require, for example, 1/2" interference for a 31/2' hole. Maurer et al. would predict a dramatically different turning radius.
Other art in the field includes Tiraspolsky, "Hydraulic Downhole Drilling Motors", pp. 193-194, which discloses a method of calculating an angle .alpha. as a function of the lengths of two sections of bent sub. Rehm, "Horizontal Drilling In Mature Oil Fields", SPE Paper No. 18709 (1988) discusses presently available curve building methods including those of Tiraspolsky (discussed above), and Taylor et al., "A Systematic Approach to Well Surveying Calculations", SPE Paper No. 3362 (1971). Talyor et al. disclose an improved method for surveying curved bore holes. A method for calculating the "dogleg" which proposes to give the same results as this appliation is disclosed by Karlsson et al., "Performance Drilling Optimization", SPE/IADC 13474 (1985).
From the above it is seen that an improved method and apparatus for determination of well turning rate is needed.